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Preparation

1 Heat the oil in a large saucepan over medium heat. Add the onion, garlic, and chile and sauté until just beginning to brown, about 5 minutes. Stir in the tomatoes and cook until most of the liquid has evaporated, 5 to 7 minutes.
2 Stir in the tomato paste, barbecue sauce, hot sauce, 1/4 cup each vinegar and sugar, the rum, 1/4 cup water, the oregano, thyme, salt, and pepper and bring to a boil, stirring to dissolve the sugar. Reduce the heat to low and simmer, uncovered, until thick and richly flavored, 20 to 30 minutes, stirring occasionally.
3 Remove from the heat and taste for seasoning, adding salt, vinegar, or sugar as necessary; the sauce should be highly seasoned. Add water if the sauce seems too thick.
4 Any unused sauce may be stored, covered, in the refrigerator for 2 to 3 weeks.
5 Makes 3 to 4 cups.